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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_autocorrelation.wasp
Title produced by software(Partial) Autocorrelation Function
Date of computationSat, 10 Nov 2012 05:51:41 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Nov/10/t1352544727snykwlkxuld5gjg.htm/, Retrieved Sat, 10 Dec 2022 05:41:28 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=187287, Retrieved Sat, 10 Dec 2022 05:41:28 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact95
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Arabica Price in ...] [2008-01-19 12:03:37] [74be16979710d4c4e7c6647856088456]
- RMPD    [(Partial) Autocorrelation Function] [Tutorial 3.2] [2012-11-10 10:51:41] [66a849a05d67389f0588cabd76580e84] [Current]
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Dataseries X:
255
280.2
299.9
339.2
374.2
393.5
389.2
381.7
375.2
369
357.4
352.1
346.5
342.9
340.3
328.3
322.9
314.3
308.9
294
285.6
281.2
280.3
278.8
274.5
270.4
263.4
259.9
258
262.7
284.7
311.3
322.1
327
331.3
333.3
321.4
327
320
314.7
316.7
314.4
321.3
318.2
307.2
301.3
287.5
277.7
274.4
258.8
253.3
251
248.4
249.5
246.1
244.5
243.6
244
240.8
249.8
248
259.4
260.5
260.8
261.3
259.5
256.6
257.9
256.5
254.2
253.3
253.8
255.5
257.1
257.3
253.2
252.8
252
250.7
252.2
250
251
253.4
251.2
255.6
261.1
258.9
259.9
261.2
264.7
267.1
266.4
267.7
268.6
267.5
268.5
268.5
270.5
270.9
270.1
269.3
269.8
270.1
264.9
263.7
264.8
263.7
255.9
276.2
360.1
380.5
373.7
369.8
366.6
359.3
345.8
326.2
324.5
328.1
327.5
324.4
316.5
310.9
301.5
291.7
290.4
287.4
277.7
281.6
288
276
272.9
283
283.3
276.8
284.5
282.7
281.2
287.4
283.1
284
285.5
289.2
292.5
296.4
305.2
303.9
311.5
316.3
316.7
322.5
317.1
309.8
303.8
290.3
293.7
291.7
296.5
289.1
288.5
293.8
297.7
305.4
302.7
302.5
303
294.5
294.1
294.5
297.1
289.4
292.4
287.9
286.6
280.5
272.4
269.2
270.6
267.3
262.5
266.8
268.8
263.1
261.2
266
262.5
265.2
261.3
253.7
249.2
239.1
236.4
235.2
245.2
246.2
247.7
251.4
253.3
254.8
250
249.3
241.5
243.3
248
253
252.9
251.5
251.6
253.5
259.8
334.1
448
445.8
445
448.2
438.2
439.8
423.4
410.8
408.4
406.7
405.9
402.7
405.1
399.6
386.5
381.4
375.2
357.7
359
355
352.7
344.4
343.8
338
339
333.3
334.4
328.3
330.7
330
331.6
351.2
389.4
410.9
442.8
462.8
466.9
461.7
439.2
430.3
416.1
402.5
397.3
403.3
395.9
387.8
378.6
377.1
370.4
362
350.3
348.2
344.6
343.5
342.8
347.6
346.6
349.5
342.1
342
342.8
339.3
348.2
333.7
334.7
354
367.7
363.3
358.4
353.1
343.1
344.6
344.4
333.9
331.7
324.3
321.2
322.4
321.7
320.5
312.8
309.7
315.6
309.7
304.6
302.5
301.5
298.8
291.3
293.6
294.6
285.9
297.6
301.1
293.8
297.7
292.9
292.1
287.2
288.2
283.8
299.9
292.4
293.3
300.8
293.7
293.1
294.4
292.1
291.9
282.5
277.9
287.5
289.2
285.6
293.2
290.8
283.1
275
287.8
287.8
287.4
284
277.8
277.6
304.9
294
300.9
324
332.9
341.6
333.4
348.2
344.7
344.7
329.3
323.5
323.2
317.4
330.1
329.2
334.9
315.8
315.4
319.6
317.3
313.8
315.8
311.3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=187287&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=187287&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=187287&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.96926918.39060
20.91465917.35440
30.85290516.18270
40.78800814.95140
50.72537713.76310
60.66732512.66160
70.61540411.67650
80.568910.79410
90.5246839.95520
100.4811119.12840
110.4395648.34010
120.3995167.58030
130.3615486.85990
140.3267376.19940
150.2991055.67510
160.2779685.27410
170.2620154.97141e-06
180.2520974.78321e-06
190.2469044.68472e-06
200.2433444.61713e-06
210.2417934.58773e-06
220.2452794.65382e-06
230.252464.79011e-06
240.2620834.97271e-06
250.2708935.13980

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.969269 & 18.3906 & 0 \tabularnewline
2 & 0.914659 & 17.3544 & 0 \tabularnewline
3 & 0.852905 & 16.1827 & 0 \tabularnewline
4 & 0.788008 & 14.9514 & 0 \tabularnewline
5 & 0.725377 & 13.7631 & 0 \tabularnewline
6 & 0.667325 & 12.6616 & 0 \tabularnewline
7 & 0.615404 & 11.6765 & 0 \tabularnewline
8 & 0.5689 & 10.7941 & 0 \tabularnewline
9 & 0.524683 & 9.9552 & 0 \tabularnewline
10 & 0.481111 & 9.1284 & 0 \tabularnewline
11 & 0.439564 & 8.3401 & 0 \tabularnewline
12 & 0.399516 & 7.5803 & 0 \tabularnewline
13 & 0.361548 & 6.8599 & 0 \tabularnewline
14 & 0.326737 & 6.1994 & 0 \tabularnewline
15 & 0.299105 & 5.6751 & 0 \tabularnewline
16 & 0.277968 & 5.2741 & 0 \tabularnewline
17 & 0.262015 & 4.9714 & 1e-06 \tabularnewline
18 & 0.252097 & 4.7832 & 1e-06 \tabularnewline
19 & 0.246904 & 4.6847 & 2e-06 \tabularnewline
20 & 0.243344 & 4.6171 & 3e-06 \tabularnewline
21 & 0.241793 & 4.5877 & 3e-06 \tabularnewline
22 & 0.245279 & 4.6538 & 2e-06 \tabularnewline
23 & 0.25246 & 4.7901 & 1e-06 \tabularnewline
24 & 0.262083 & 4.9727 & 1e-06 \tabularnewline
25 & 0.270893 & 5.1398 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=187287&T=1

[TABLE]
[ROW][C]Autocorrelation Function[/C][/ROW]
[ROW][C]Time lag k[/C][C]ACF(k)[/C][C]T-STAT[/C][C]P-value[/C][/ROW]
[ROW][C]1[/C][C]0.969269[/C][C]18.3906[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.914659[/C][C]17.3544[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.852905[/C][C]16.1827[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.788008[/C][C]14.9514[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.725377[/C][C]13.7631[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.667325[/C][C]12.6616[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.615404[/C][C]11.6765[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.5689[/C][C]10.7941[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.524683[/C][C]9.9552[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.481111[/C][C]9.1284[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.439564[/C][C]8.3401[/C][C]0[/C][/ROW]
[ROW][C]12[/C][C]0.399516[/C][C]7.5803[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.361548[/C][C]6.8599[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.326737[/C][C]6.1994[/C][C]0[/C][/ROW]
[ROW][C]15[/C][C]0.299105[/C][C]5.6751[/C][C]0[/C][/ROW]
[ROW][C]16[/C][C]0.277968[/C][C]5.2741[/C][C]0[/C][/ROW]
[ROW][C]17[/C][C]0.262015[/C][C]4.9714[/C][C]1e-06[/C][/ROW]
[ROW][C]18[/C][C]0.252097[/C][C]4.7832[/C][C]1e-06[/C][/ROW]
[ROW][C]19[/C][C]0.246904[/C][C]4.6847[/C][C]2e-06[/C][/ROW]
[ROW][C]20[/C][C]0.243344[/C][C]4.6171[/C][C]3e-06[/C][/ROW]
[ROW][C]21[/C][C]0.241793[/C][C]4.5877[/C][C]3e-06[/C][/ROW]
[ROW][C]22[/C][C]0.245279[/C][C]4.6538[/C][C]2e-06[/C][/ROW]
[ROW][C]23[/C][C]0.25246[/C][C]4.7901[/C][C]1e-06[/C][/ROW]
[ROW][C]24[/C][C]0.262083[/C][C]4.9727[/C][C]1e-06[/C][/ROW]
[ROW][C]25[/C][C]0.270893[/C][C]5.1398[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=187287&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=187287&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Autocorrelation Function
Time lag kACF(k)T-STATP-value
10.96926918.39060
20.91465917.35440
30.85290516.18270
40.78800814.95140
50.72537713.76310
60.66732512.66160
70.61540411.67650
80.568910.79410
90.5246839.95520
100.4811119.12840
110.4395648.34010
120.3995167.58030
130.3615486.85990
140.3267376.19940
150.2991055.67510
160.2779685.27410
170.2620154.97141e-06
180.2520974.78321e-06
190.2469044.68472e-06
200.2433444.61713e-06
210.2417934.58773e-06
220.2452794.65382e-06
230.252464.79011e-06
240.2620834.97271e-06
250.2708935.13980







Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.96926918.39060
2-0.410181-7.78260
30.0056380.1070.457432
4-0.059461-1.12820.129996
50.036490.69240.24458
60.0087070.16520.434439
70.0309540.58730.278681
8-0.003201-0.06070.475803
9-0.042486-0.80610.210356
10-0.031707-0.60160.273912
110.0119580.22690.410318
12-0.019858-0.37680.353281
130.005510.10450.458396
140.008320.15790.437329
150.0794661.50780.066245
160.0079230.15030.440292
170.0191850.3640.358032
180.0475360.90190.183847
190.0182930.34710.364365
20-0.014594-0.27690.391004
210.0384690.72990.232965
220.0849811.61240.053875
230.0175350.33270.369775
240.0220940.41920.33766
25-0.028576-0.54220.294012

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.969269 & 18.3906 & 0 \tabularnewline
2 & -0.410181 & -7.7826 & 0 \tabularnewline
3 & 0.005638 & 0.107 & 0.457432 \tabularnewline
4 & -0.059461 & -1.1282 & 0.129996 \tabularnewline
5 & 0.03649 & 0.6924 & 0.24458 \tabularnewline
6 & 0.008707 & 0.1652 & 0.434439 \tabularnewline
7 & 0.030954 & 0.5873 & 0.278681 \tabularnewline
8 & -0.003201 & -0.0607 & 0.475803 \tabularnewline
9 & -0.042486 & -0.8061 & 0.210356 \tabularnewline
10 & -0.031707 & -0.6016 & 0.273912 \tabularnewline
11 & 0.011958 & 0.2269 & 0.410318 \tabularnewline
12 & -0.019858 & -0.3768 & 0.353281 \tabularnewline
13 & 0.00551 & 0.1045 & 0.458396 \tabularnewline
14 & 0.00832 & 0.1579 & 0.437329 \tabularnewline
15 & 0.079466 & 1.5078 & 0.066245 \tabularnewline
16 & 0.007923 & 0.1503 & 0.440292 \tabularnewline
17 & 0.019185 & 0.364 & 0.358032 \tabularnewline
18 & 0.047536 & 0.9019 & 0.183847 \tabularnewline
19 & 0.018293 & 0.3471 & 0.364365 \tabularnewline
20 & -0.014594 & -0.2769 & 0.391004 \tabularnewline
21 & 0.038469 & 0.7299 & 0.232965 \tabularnewline
22 & 0.084981 & 1.6124 & 0.053875 \tabularnewline
23 & 0.017535 & 0.3327 & 0.369775 \tabularnewline
24 & 0.022094 & 0.4192 & 0.33766 \tabularnewline
25 & -0.028576 & -0.5422 & 0.294012 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=187287&T=2

[TABLE]
[ROW][C]Partial Autocorrelation Function[/C][/ROW]
[ROW][C]Time lag k[/C][C]PACF(k)[/C][C]T-STAT[/C][C]P-value[/C][/ROW]
[ROW][C]1[/C][C]0.969269[/C][C]18.3906[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.410181[/C][C]-7.7826[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.005638[/C][C]0.107[/C][C]0.457432[/C][/ROW]
[ROW][C]4[/C][C]-0.059461[/C][C]-1.1282[/C][C]0.129996[/C][/ROW]
[ROW][C]5[/C][C]0.03649[/C][C]0.6924[/C][C]0.24458[/C][/ROW]
[ROW][C]6[/C][C]0.008707[/C][C]0.1652[/C][C]0.434439[/C][/ROW]
[ROW][C]7[/C][C]0.030954[/C][C]0.5873[/C][C]0.278681[/C][/ROW]
[ROW][C]8[/C][C]-0.003201[/C][C]-0.0607[/C][C]0.475803[/C][/ROW]
[ROW][C]9[/C][C]-0.042486[/C][C]-0.8061[/C][C]0.210356[/C][/ROW]
[ROW][C]10[/C][C]-0.031707[/C][C]-0.6016[/C][C]0.273912[/C][/ROW]
[ROW][C]11[/C][C]0.011958[/C][C]0.2269[/C][C]0.410318[/C][/ROW]
[ROW][C]12[/C][C]-0.019858[/C][C]-0.3768[/C][C]0.353281[/C][/ROW]
[ROW][C]13[/C][C]0.00551[/C][C]0.1045[/C][C]0.458396[/C][/ROW]
[ROW][C]14[/C][C]0.00832[/C][C]0.1579[/C][C]0.437329[/C][/ROW]
[ROW][C]15[/C][C]0.079466[/C][C]1.5078[/C][C]0.066245[/C][/ROW]
[ROW][C]16[/C][C]0.007923[/C][C]0.1503[/C][C]0.440292[/C][/ROW]
[ROW][C]17[/C][C]0.019185[/C][C]0.364[/C][C]0.358032[/C][/ROW]
[ROW][C]18[/C][C]0.047536[/C][C]0.9019[/C][C]0.183847[/C][/ROW]
[ROW][C]19[/C][C]0.018293[/C][C]0.3471[/C][C]0.364365[/C][/ROW]
[ROW][C]20[/C][C]-0.014594[/C][C]-0.2769[/C][C]0.391004[/C][/ROW]
[ROW][C]21[/C][C]0.038469[/C][C]0.7299[/C][C]0.232965[/C][/ROW]
[ROW][C]22[/C][C]0.084981[/C][C]1.6124[/C][C]0.053875[/C][/ROW]
[ROW][C]23[/C][C]0.017535[/C][C]0.3327[/C][C]0.369775[/C][/ROW]
[ROW][C]24[/C][C]0.022094[/C][C]0.4192[/C][C]0.33766[/C][/ROW]
[ROW][C]25[/C][C]-0.028576[/C][C]-0.5422[/C][C]0.294012[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=187287&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=187287&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Partial Autocorrelation Function
Time lag kPACF(k)T-STATP-value
10.96926918.39060
2-0.410181-7.78260
30.0056380.1070.457432
4-0.059461-1.12820.129996
50.036490.69240.24458
60.0087070.16520.434439
70.0309540.58730.278681
8-0.003201-0.06070.475803
9-0.042486-0.80610.210356
10-0.031707-0.60160.273912
110.0119580.22690.410318
12-0.019858-0.37680.353281
130.005510.10450.458396
140.008320.15790.437329
150.0794661.50780.066245
160.0079230.15030.440292
170.0191850.3640.358032
180.0475360.90190.183847
190.0182930.34710.364365
20-0.014594-0.27690.391004
210.0384690.72990.232965
220.0849811.61240.053875
230.0175350.33270.369775
240.0220940.41920.33766
25-0.028576-0.54220.294012



Parameters (Session):
par1 = 12 ;
Parameters (R input):
par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;
R code (references can be found in the software module):
if (par1 == 'Default') {
par1 = 10*log10(length(x))
} else {
par1 <- as.numeric(par1)
}
par2 <- as.numeric(par2)
par3 <- as.numeric(par3)
par4 <- as.numeric(par4)
par5 <- as.numeric(par5)
if (par6 == 'White Noise') par6 <- 'white' else par6 <- 'ma'
par7 <- as.numeric(par7)
if (par8 != '') par8 <- as.numeric(par8)
ox <- x
if (par8 == '') {
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
} else {
x <- log(x,base=par8)
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='picts.png')
op <- par(mfrow=c(2,1))
plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')
if (par8=='') {
mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
} else {
mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
}
plot(x,type='l', main=mytitle,xlab='time',ylab='value')
par(op)
dev.off()
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)
dev.off()
(myacf <- c(racf$acf))
(mypacf <- c(rpacf$acf))
lengthx <- length(x)
sqrtn <- sqrt(lengthx)
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Autocorrelation Function',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Time lag k',header=TRUE)
a<-table.element(a,hyperlink('basics.htm','ACF(k)','click here for more information about the Autocorrelation Function'),header=TRUE)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,'P-value',header=TRUE)
a<-table.row.end(a)
for (i in 2:(par1+1)) {
a<-table.row.start(a)
a<-table.element(a,i-1,header=TRUE)
a<-table.element(a,round(myacf[i],6))
mytstat <- myacf[i]*sqrtn
a<-table.element(a,round(mytstat,4))
a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Partial Autocorrelation Function',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Time lag k',header=TRUE)
a<-table.element(a,hyperlink('basics.htm','PACF(k)','click here for more information about the Partial Autocorrelation Function'),header=TRUE)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,'P-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:par1) {
a<-table.row.start(a)
a<-table.element(a,i,header=TRUE)
a<-table.element(a,round(mypacf[i],6))
mytstat <- mypacf[i]*sqrtn
a<-table.element(a,round(mytstat,4))
a<-table.element(a,round(1-pt(abs(mytstat),lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')